An improved high-order scheme for DNS of low Mach number turbulent reacting flows based on stiff chemistry solver

Yu, Rixin; Yu, Jiangfei; Bai, Xue‐Song

doi:10.1016/j.jcp.2012.05.006

Cited by 57 publications

(28 citation statements)

References 33 publications

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“…Simulations were performed using a simplified in-house DNS solver [30] developed for low-Mach-number reacting flows and equipped with a standalone stiff chemistry solver for a general kinetic mechanism. The solver was already applied to various reacting flow systems [31][32][33][34].…”

Section: Numerical Methods and Simulation Conditionsmentioning

confidence: 99%

Direct numerical simulation study of statistically stationary propagation of a reaction wave in homogeneous turbulence

Lipatnikov

2017

Phys. Rev. E

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A three-dimensional (3D) direct numerical simulation (DNS) study of the propagation of a reaction wave in forced, constant-density, statistically stationary, homogeneous, isotropic turbulence is performed by solving Navier-Stokes and reaction-diffusion equations at various (from 0.5 to 10) ratios of the rms turbulent velocity U to the laminar wave speed, various (from 2.1 to 12.5) ratios of an integral length scale of the turbulence to the laminar wave thickness, and two Zeldovich numbers Ze = 6.0 and 17.1. Accordingly, the Damköhler and Karlovitz numbers are varied from 0.2 to 25.1 and from 0.4 to 36.2, respectively. Contrary to an earlier DNS study of self-propagation of an infinitely thin front in statistically the same turbulence, the bending of dependencies of the mean wave speed on U is simulated in the case of a nonzero thickness of the local reaction wave. The bending effect is argued to be controlled by inefficiency of the smallest scale turbulent eddies in wrinkling the reaction-zone surface, because such small-scale wrinkles are rapidly smoothed out by molecular transport within the local reaction wave.

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Section: Numerical Methods and Simulation Conditionsmentioning

confidence: 99%

Direct numerical simulation study of statistically stationary propagation of a reaction wave in homogeneous turbulence

Lipatnikov

2017

Phys. Rev. E

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“…The lagging errors introduced by the operator splitting treatment are unimportant for steady-state configurations, but may be substantial in some circumstances, for instance in the proximity of unsteady premixed flame fronts [3,33], and become more severe when running with larger time step sizes. The effects of these errors have been the subject of many previous studies [33][34][35][36][37], and have been found to be case-dependent. Note that, with the application of these techniques, the resulting Ordinary Differential Equations (ODE) associated with the chemistry (instead of the coupled PDEs) remain stiff.…”

Section: Introductionmentioning

confidence: 99%

“…To alleviate the high computational overhead associated with the integration of these stiff ODEs, methods relying on implicit numerical schemes based on Backward-Differentiation Formulas (BDF) have been developed [38,39] and implemented in packages such as VODE [40] and DASSL [41,42]. These packages integrate stiff chemical kinetics using BDFs with a modified iterative Newton procedure [41][42][43][44], and have been widely adopted in numerical simulations of chemically reacting flows [3,33,34]. Despite the significant computational efficiency gain brought by the stiff chemistry integration techniques discussed above, it is important to recall that these techniques are designed for time-dependent ODE systems (and not PDE), which arise from the application of time-splitting techniques to separate the reactive (chemical kinetic) part of the PDE system (species transport equations) from the convective-diffusive part [45].…”

Section: Introductionmentioning

confidence: 99%

A computationally-efficient, semi-implicit, iterative method for the time-integration of reacting flows with stiff chemistry

Savard

Xuan

Bobbitt

et al. 2015

Journal of Computational Physics

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Please cite this article in press as: B. Savard et al., A computationally-efficient, semi-implicit, iterative method for the time-integration of reacting flows with stiff chemistry, J. Comput. Phys. (2015), http://dx. Abstract A semi-implicit preconditioned iterative method is proposed for the time-integration of the stiff chemistry in simulations of unsteady reacting flows, such as turbulent flames, using detailed chemical kinetic mechanisms. Emphasis is placed on the simultaneous treatment of convection, diffusion, and chemistry, without using operator splitting techniques. The preconditioner corresponds to an approximation of the diagonal of the chemical Jacobian. Upon convergence of the sub-iterations, the fully-implicit, second-order time-accurate, Crank-Nicolson formulation is recovered. Performance of the proposed method is tested theoretically and numerically on one-dimensional laminar and three-dimensional high Karlovitz turbulent premixed n-heptane/air flames. The species lifetimes contained in the diagonal preconditioner are found to capture all critical small chemical timescales, such that the largest stable time step size for the simulation of the turbulent flame with the proposed method is limited by the convective CFL, rather than chemistry. The theoretical and numerical stability limits are in good agreement and are independent of the number of sub-iterations. The results indicate that the overall procedure is second-order accurate in time, free of lagging errors, and the cost per iteration is similar to that of an explicit time integration. The theoretical analysis is extended to a wide range of flames (premixed and non-premixed), unburnt conditions, fuels, and chemical mechanisms. In all cases, the proposed method is found (theoretically) to be stable and to provide good convergence rate for the sub-iterations up to a time step size larger than 1 μs. This makes the proposed method ideal for the simulation of turbulent flames.

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“…Details of the governing equations solved and the numerical methods are described in Ref. [13], where evaluations of the numerical solver are provided. A short description of the numerical method is given below, focusing on key features of the solver and new implementations of the method accounting for the compression effect.…”

Section: Methodsmentioning

confidence: 99%

“…The original DNS solver was designed for constant volume domain simulation based on fixed grid [13]. To account for the pressure rise due to piston motion while still based on the constant volume domain framework, the original conservation equations are modified by employing a temporally evolving but spatially uniform source term.…”

Section: Methodsmentioning

confidence: 99%

Detailed numerical simulation of syngas combustion under partially premixed combustion engine conditions

Zhang

Bai

2012

International Journal of Hydrogen Energy

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An improved high-order scheme for DNS of low Mach number turbulent reacting flows based on stiff chemistry solver

Cited by 57 publications

References 33 publications

Direct numerical simulation study of statistically stationary propagation of a reaction wave in homogeneous turbulence

Direct numerical simulation study of statistically stationary propagation of a reaction wave in homogeneous turbulence

A computationally-efficient, semi-implicit, iterative method for the time-integration of reacting flows with stiff chemistry

Detailed numerical simulation of syngas combustion under partially premixed combustion engine conditions

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